On the server, right-click on the folder/share and left-click on Properties. In the Properties window, click on the Security tab, then click on the Advanced button. In the Advanced Properties window, click on the Auditing tab. From there, click on the Add button and then add whatever users or groups you want to monitor. You can choose all users, or just specific users depending on what the situation requires (you can use Everyone or Domain Users if you want to monitor everyone). After you have the users/groups selected, click OK and it will open a window titled "Auditing Entry". In this window, select the options that you want to monitor such as List Folder, Delete, and Delete Subfolders and Files, to record each time someone opens the folder and each time someone deletes a file, (or just click Full Control in both columns to audit everything if you want to do that) and then click OK three times to save the changes.
Any access to the share that meets the parameters you selected on the Auditing page will then show up in the Event Log on the server so you'll be able to see exactly how and when those files are accessed or deleted, and by whom.